Abstract:

A two-dimensional inverse problem of determination of wave propagation velocity and kernel in a viscoelasticity equation for a weakly horizontally inhomogeneous medium is presented. The direct
initial-boundary value problem for the displacement function contains zero initial data and the Neumann condition of a special form. The source of wave propagation is the Dirac delta function. For inverse problem statement the displacement Fourier transform  is given at the border of the half-space. It is assumed that the wave propagation velocity, kernel and displacement decom-poses into an asymptotic series. In this paper, we construct a method for determining unknowns functions with an accuracy of $O(\varepsilon^2)$, where $\varepsilon$ is a small parameter. The theorems of global unique solvability and stability are proved.